Student Handbook: Learning Outcomes

All students will be appraised of the departmental learning outcomes objectives which are as follows:

Upon the completion of the core curriculum in Mathematics, the student should be able to:

1) Analyze polynomial and transcendental functions of one or more variables with respect to:

a) operations of functions, graphs, existence of inverse functionsb) existence of limitsc) continuity, differentiability (both explicit and implicit) and partial differentiation.d) integrability with techniques of integratione) representation of functions through infinite seriesf) interpretation and summary of information from graphs of functionsg) be able to prove limit theorems in simple cases by using Epsilon - Delta methods

2) Demonstrate an understanding for the applications of the derivative and the integral in:

a) linear systems and the solution of such systemsb) special types and properties of matricesc) elementary matrices and their importance in proofsd) transformationse) vector spaces, determinants, and eigenvaluesf) abstract inner product spaces

a) principles of logicb) methods of proof: proof by induction, contradiction, contrapositionc) understand the axiomatic development of consistent mathematical systems and the importance of counter examplesd) interpret mathematical statements distinguishing hypotheses and conclusionse) distinguish between conjecture and rigorous mathematical proof

Upon the completion of the Mathematics Program, the student should be able to:

6) Demonstrate quantitative literacy:

a) be able to analyze, interpret, and present data in a logical and scientific manner.b) know basic counting methods, and basic knowledge of statistics and probability

7) Demonstrate an understanding of the principles and techniques of applying mathematics to real world problems:

a) use techniques of linear algebra and differential equations to solve various applied problemsb) understand the importance and widespread existence of nonlinear problems and the role of the linear theory in developing insight into these problemsc) grasp the concept of "dynamical" systems and their importance in comparison to "static" problems

8) Understand the role of the computer in mathematics by implementing and understanding the importance and limitations of algorithms for:

a) numerical methods for approximating integrals, series and numbersb) different methods for graphing continuous and discontinuous functions in two and three dimensionsc) numerical methods for approximating solutions of linear systems and differential equations

9) Communicate clearly and effectively in an organized fashion the basic concepts and principles of mathematics, from calculus to modern applications and theory:

a) communicate, in both oral and written fashion, mathematical concepts and methods in a precise mannerb) present historical perspectives and implications of mathematical ideasc) understand research in mathematics by actively doing research in a specific aread) analyze some application problems using modeling techniques to observe patterns, interconnections, and underlying structures